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Explicit Difference Schemes for Nonlinear Differential Functional Parabolic Equations with Mixed Derivatives - Convergence Analysis

100%

Poliński A.

Commentationes Mathematicae

2005

tom 45

nr 2

We study the initial-value problem for parabolic equations with mixed partial derivatives and constant coefficients, and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.

Thermal ablation modeling via the bioheat equation and its numerical treatment

51%

Bartłomiejczyk A., Leszczyński H., Poliński A.

Applicationes Mathematicae

2015

tom 42

nr 1

1-12

The phenomenon of thermal ablation is described by Pennes' bioheat equation. This model is based on Newton's law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Commentationes Mathematicae

2 Poliński A.

1 Bartłomiejczyk A.

1 Leszczyński H.

1 2015

1 2005

Wyniki wyszukiwania

Explicit Difference Schemes for Nonlinear Differential Functional Parabolic Equations with Mixed Derivatives - Convergence Analysis

Thermal ablation modeling via the bioheat equation and its numerical treatment